The probabilities of a student getting I. II and III class in an examination are \(\frac { 1 }{ 10 } ,\frac { 3 }{ 5 } \) and \(\frac { 1 }{ 4 } \) respectively. The probability that the student fails in the examination is

(a)

\(\frac { 197 }{ 200 } \)

(b)

\(\frac { 27 }{ 100 } \)

(c)

\(\frac { 83 }{ 100 } \)

(d)

none of these

Three integers are chosen at random from the first 20 integers. The probability that their product is even is

(a)

\(\frac { 2 }{ 19 } \)

(b)

\(\frac { 3 }{ 19 } \)

(c)

\(\frac { 17 }{ 19 } \)

(d)

\(\frac { 4 }{ 19 } \)

The probability that in a year of 22^nd century, chosen at random there will be 53 Sundays is

(a)

\(\frac { 3 }{ 28 } \)

(b)

\(\frac { 2 }{ 28 } \)

(c)

\(\frac { 7 }{ 28 } \)

(d)

\(\frac { 5 }{ 28 } \)

If A and B are two events such that \(P(A\cap B)=\frac { 7 }{ 10 } \) and P(B) = \(\frac { 17 }{ 20 } \) , then P(A/B) =

(a)

\(\frac { 14 }{ 17 } \)

(b)

\(\frac { 17 }{ 20 } \)

(c)

\(\frac { 7 }{ 8 } \)

(d)

\(\frac { 1 }{ 8 } \)

Let A and B be two events such that P(A) = 0.6, P(B) = 0.2 and P(A/B) = 0.5, Then P(\(\bar { A } /\bar { B } \)) is

(a)

\(\frac { 1 }{ 10 } \)

(b)

\(\frac { 3 }{ 10 } \)

(c)

\(\frac { 3 }{ 8 } \)

(d)

\(\frac { 6 }{ 7 } \)